通过拉盖尔展开估计多元广义伽玛卷积
Estimation of multivariate generalized gamma convolutions through Laguerre expansions
AI总结：
本文通过拉盖尔展开方法，为多元广义伽玛卷积提供了高效的估计程序，并展示了其在稳定性上的优势。
摘要：
广义伽玛卷积类分布出现在Thorin的工作中，当时他试图寻找对数正态分布和帕累托分布的无限可分性。尽管这些分布已经在单变量情况下被广泛研究，但多元情况以及由此产生的依赖结构在文献中却很少受到关注。此外，最近只有一种针对单变量情况的投影程序被构造出来，而没有可用的估计程序。通过将多元广义伽玛卷积的密度展开为张量化的拉盖尔基，我们填补了这一空白，为单变量和多元情况提供了高效的估计程序。我们提供了一些关于这些程序性能的见解，并给出了多元伽玛卷积密度的收敛级数，证明其比Moschopoulos和Mathai的单变量级数更加稳定。我们还进一步讨论了一些例子。
英文摘要：
The generalized gamma convolutions class of distributions appeared in Thorin's work while looking for the infinite divisibility of the log-Normal and Pareto distributions. Although these distributions have been extensively studied in the univariate case, the multivariate case and the dependence structures that can arise from it have received little interest in the literature. Furthermore, only one projection procedure for the univariate case was recently constructed, and no estimation procedures are available. By expanding the densities of multivariate generalized gamma convolutions into a tensorized Laguerre basis, we bridge the gap and provide performant estimation procedures for both the univariate and multivariate cases. We provide some insights about performance of these procedures, and a convergent series for the density of multivariate gamma convolutions, which is shown to be more stable than Moschopoulos's and Mathai's univariate series. We furthermore discuss some examples.
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